The super Mumford form and Sato Grassmannian

Maxwell, Katherine A.

doi:10.1016/j.geomphys.2022.104604

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The super Mumford form and Sato Grassmannian

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Maxwell, Katherine A.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.geomphys.2022.104604
(Publisher version)

https://doi.org/10.48550/arXiv.2002.06625
(Preprint)

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Citation

Maxwell, K. A. (2022). The super Mumford form and Sato Grassmannian. Journal of Geometry and Physics, 180: 104604. doi:10.1016/j.geomphys.2022.104604.

Cite as: https://hdl.handle.net/21.11116/0000-000A-DB9B-1

Abstract

We describe a supersymmetric generalization of the construction of Kontsevich
and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between
the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our
main result is the existence of a flat holomorphic connection on the line
bundle $\lambda_{3/2}\otimes\lambda_{1/2}^{-5}$ on the moduli space of triples:
a super Riemann surface, a Neveu-Schwarz puncture, and a formal coordinate
system. We also prove a superconformal Noether normalization lemma for families
of super Riemann surfaces.